2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78673We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed two families of plane curves with second order contact at the envelope.25pagesGeometric TopologyTopological rigidity for certain families of differentiable plane curvestext